Question

Assume you are to receive a 10-year annuity with annual payments of $1000. The first payment will be received at the end of Year 1, and the last payment will be received at the end of Year 10. You will invest each payment in an account that pays 9 percent compounded annually. Although the annuity payments stop at the end of year 10, you will not withdraw any money from the account until 25 years from today, and the account will continue to earn 9% for the entire 25-year period. What will be the value in your account at the end of Year 25 (rounded to the nearest dollar)? Select one: a. $48,000 b. $35,967 c. $48,359 d. $55,340 Clear my choice Question 4

Answer 1

d. $55,340

Step-by-step explanation:

You begin to receive the annuity at the end of the year 1, so its begin to capitalize on year 2 because the first year

there is no money to capitalize.

The second year begin to apply over the first annuity the interest payment,the next ten 10 years from 2 to 11 the deposits start to capitalize compounded anually at 9% of interest.

Compound interest, means that each time that the account generate interests, this total amount apply to the next period as basis to calculate the next interests, not only grows the interest payment over the initial capital if not over the past interest generated.

At the end of the 25 years you will have $55,340 in the account available.

$ 1,000 $ 1,090 2 Year

$ 1,000 $ 2,278 3 Year

$ 1,000 $ 3,573 4 Year

$ 1,000 $ 4,985 5 Year

$ 1,000 $ 6,523 6 Year

$ 1,000 $ 8,200 7 Year

$ 1,000 $ 10,028 8 Year

$ 1,000 $ 12,021 9 Year

$ 1,000 $ 14,193 10 Year

$ 1,000 $ 16,560 11 Year

$ 18,051 12 Year

$ 19,675 13 Year

$ 21,446 14 Year

$ 23,376 15 Year

$ 25,480 16 Year

$ 27,773 17 Year

$ 30,273 18 Year

$ 32,997 19 Year

$ 35,967 20 Year

$ 39,204 21 Year

$ 42,733 22 Year

$ 46,579 23 Year

$ 50,771 24 Year

$ 55,340 25 Year